Elementary Logic
PHIL 105-302
Intersession 2013
MTWHF 10:00 – 12:00
ASA0118C
Steven A. Miller
Day 1
Syllabus Highlights
Instructor: Steven A. Miller
Office hours: MW – 12:30-2:00
Faner 3026
Contact info: mllrstvn@siu.edu
847-312-2737
Syllabus Highlights, cont.
Texts:
Schaum’s Outline of Logic, 2nd ed.
Priest’s Logic: A Very Short Introduction
Westin’s A Rulebook for Arguments, 4th ed.
All three texts are “required.”
Syllabus Highlights, cont., cont.
Policies:
1) Attendance is optional.
2) Electronic devices should not distract.
3) Conversational abuse and distractions are
also unwelcome.
4) Papers must conform to formatting
standards.
5) Academic dishonesty will result in harsh
penalties, likely involving failure.
Syllabus Highlights, cont., cont., cont.
Grading:
Thursday quizzes (4, 50 points each) – 25%
Friday exams (4, 100 points each) – 50%
Short papers (2, 100 points each) – 25%
All points are equally weighted. Except
with prior arrangement, late work will not
be accepted. There will be no curving or
extra credit.
There is no homework.
Syllabus Highlights, cont., cont., etc.
Schedule:
Week
Week
Week
Week
1
2
3
4
–
–
–
–
basics, truth table / tree proofs
propositional calculus
categorical and predicate logic
informal logic / rhetoric
“Elementary Logic”
“Elementary”
– basic, straightforward, obvious
– e.g. “Elementary, my dear Watson.”
“Logic”
– unemotional, cool, detached
– commonsensical beliefs
– reasoning
What is logic?
“Being reasonable”
Logic, then, is reasoning well.
It is not necessarily an account of how
we do reason but rather an account
of how we should do so.
Should!?
One should reason this way because…
1) It’s truth-preserving.
2) It’s convincing.
3) It’s fair.
Arguments
The argument is this course’s prime focus.
So, what’s an argument?
Definition: “An argument is a sequence of
statements of which one is intended as a
conclusion and the others, the premises, are
intended to prove or at least provide some
evidence for the conclusion” (S, p. 1).
Words, words, words.
“An argument is a sequence of
statements of which one is intended
as a conclusion and the others, the
premises, are intended to prove or at
least provide some evidence for the
conclusion.”
Statement
A sentence, usually in the declarative
mood, that has or could have a
truth-value.
Truth-value: A sentence’s being either
true or false.
Statement
True – the statement is the case
“All squares are rectangles.”
“Barack Obama is the president.”
“I am called ‘Steven’.”
False – the statement is not the case
“All dogs are reptiles.”
“No one here is older than 5.”
Are these statements?
“Carbondale is south of Chicago.”
“The fire-truck is red.”
“Grapes are orange.”
“My father is an electrician.”
“What’s your favorite food?”
“Stop it!”
INTERMISSION
(Try our fresh-popped popcorn and refreshing soda!)
Argument definition
“An argument is a sequence of
statements of which one is intended
as a conclusion and the others, the
premises, are intended to prove or at
least provide some evidence for the
conclusion.”
Conclusion
A statement that one is trying to show
is true, through support of premises.
For our purposes, all arguments have
only one conclusion. (They may,
however, have multiple “subconclusions.”)
Conclusion “signaling” words
thus
therefore
hence
consequently
as a result
so
accordingly
clearly
must be that
shows that
conclude that follows that
for this reason
Premises
A statement that is offered as
evidence for the conclusion.
For our purposes, all arguments have
at least one premise.
Premise “signaling” words
because
given that
furthermore
since
for
moreover
as indicated
due to
besides
for example
owing to
in addition
for the reason
what’s more
after all
in fact
this can be seen from
Sample argument
1) All cats are fluffy.
2) BabyFritz is a cat.
3) Therefore, BabyFritz is fluffy.
Which line(s) is / are the conclusion?
Which line(s) is / are the premise(s)?
Sample argument
1) BabyFritz is fluffy.
2) All cats are fluffy.
3) BabyFritz is a cat.
The conclusion may appear anywhere
in the argument.
The conclusion won’t always be
signaled.
Sample argument
1)
2)
3)
4)
5)
All cats are fluffy.
All fluffy things are soft.
BabyFritz is a cat.
So, BabyFritz is fluffy.
Therefore, BabyFritz is soft.
Line 4 appears as a conclusion, but its
function in the argument is as a further
premise. We call these premises “subconclusions.”
Argument definition
“An argument is a sequence of
statements of which one is intended
as a conclusion and the others, the
premises, are intended to prove or at
least provide some evidence for the
conclusion.”
Is it an argument?
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
Is it an argument?
All men are mortal.
Socrates is a man.
The Cardinals are the worst team.
Therefore, Socrates is mortal.
Is it an argument?
91% of Polish people are Catholic.
Pitor is a Polish person.
We can conclude that Pitor is likely Catholic.
Is it an argument?
You are mean to me.
We fight too much.
Therefore, why don’t we break up?
Is it an argument?
2x + 1 = 5
2x = 4
Therefore, x = 2.
Is it an argument?
All Quakers are pirates.
The Cardinals are the best team.
Grass is painted nightly by gnomes.
Therefore, blackboards are black.
Argument recap(itulation)
1) At least two statements.
2) One (and only one) of which is the
conclusion.
3) Some sort of relationship of support
intended between the conclusion
and the other statement(s).
Diagramming
Schaum pages 7-20.
A numerical / graphical strategy for
understanding the relationships
between statements.
If you’re having trouble finding
conclusion / seeing implications, try
it out.